# Prize crossnumber, Issue 14

Our original prize crossnumber is featured on pages 60 and 61 of Issue 14.

### Rules

• The down clues are provided as normal. The across clues are provided in alphabetical order without their clue numbers or lengths.
• Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. Solvers may wish to use the OEIS, Wikipedia, Python, a book of log tables, etc to (for example) obtain a list of cube numbers, but no programming should be necessary to solve the puzzle. As usual, no numbers begin with 0.
• One randomly selected correct answer will win a £100 Maths Gear goody bag, including non-transitive dice, a Festival of the Spoken Nerd DVD, and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. Maths Gear is a website that sells nerdy things worldwide, with free UK shipping.
• To enter, submit the sum of the across entries using this form by 14 March 2022. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 May 2022.

# Dear Dirichlet, Issue 14

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to deardirichlet@chalkdustmagazine.com.

### Dear Dirichlet,

I’m not much of a football fan but I enjoyed the Euros over the summer. I’d like to learn a bit more about the sport and maybe support a club or two. Any suggestions?

— Steve Orgizovic, Unknown, possibly kidnapped

# Cryptic crossword, Issue 14

Cryptic #2, set by Humbug:

### Across clues

• 1. $\int2x\,\mathrm{d}x-x^2$, $6-6$, $6-10$, $1 – \text{O}$, $a\div h$. (6)
• 4. Ape rambling by grand mountain. (4)
• 7. How much is contained inside Far East?. (4)
• 8. Fifty-one first, million second, six third, until eventually tending to this. (5)
• 10. Limits of nonangle and torus can be folded up to make 3D shapes. (4)
• 11. $\nabla\cdot(\text{kinetic energy}-y+t)$ is limitless. (9)
• 14. Knight on the telephone regularly called after band. (6)
• 15. Ball concealed by cusp, he realises. (6)
• 17. Romeo, for example, coming to grips with TeX archive, initially loads editing box. (9)
• 20. Boundary of zero-free area contains trivial origin‽ (4)
• 22. A principle of astronomy leads people home again. (5)
• 24. Contentless sudoku reworded to become irrational. (4)
• 25. Head left, alternatively split in two. (4)
• 26. Carla’s confused without direction. (6)

### Down clues

• 1. Disoriented duck halts magazine. (9)
• 2. How quickly deep end fills up. (5)
• 3. 50 and 5 dividing $3\times2.718$, adding $n$ makes a prime. (6)
• 4. Endless DPhil leads to a solution of $x^2-x-1=0$. (3)
• 5. Quadrilateral built from potassium, iodine and tellurium. (4)
• 6. $x$, for example, starts after eleven seconds. (4)
• 8. Function that can be split into smaller pieces using axes. (3)
• 9. For example, $[0, 5)\in T$ precedes perturbed real around five?. (8)
• 12. Calculates the area of misshapen triangle. (8)
• 13. Dreamer in disarray produces rest. (9)
• 16. Timeless tangles might be sharp?. (6)
• 18. Third part of ratio mnemonic initially takes odd approach. (3)
• 19. Is a bit of curve quality?. (5)
• 20. Heading for Zambia Egypt result: nil-nil. (4)
• 21. More complex than hyperbolic function. (4)
• 23. Shared divisor ends much algebraic faff. (1,1,1)

# Issue 13 launch art project

We are very excited to launch issue 13 of Chalkdust which we have jam packed with articles lovingly crafted by our authors and editors. This issue is something of an homage to the late great John Conway who is featured as our significant figure. The issue also includes some favourite mathematical games and cellular automata, both of which Conway was very interested in.

In order to celebrate the release of Chalkdust issue 13, we have decided to do something a little different. Alas we cannot yet invite you to join us for an in-person celebration, but we thought it would be fun to join with you in a little community art and maths project inspired by our cover feature for this issue on cellular automata. In short, an automaton is a simple machine which follows a set of rules, perhaps to produce a pattern of coloured squares. These patterns can turn out to be surprisingly complex given the unassuming rules which generate them. You should read up about elementary cellular automata in our cover article, before reading on below.

## A marriage of maths and art

What is it exactly we would like you to do? Produce a piece of art inspired by a cellular automaton. Quite deliberately we are not being proscriptive about the medium of the art, or exactly which automaton you choose. We would however recommend that you stick to an automaton which is a variation on the elementary automata discussed in our cover feature, in particular a one-dimensional automaton which allows you to represent the time-evolution of the pattern in two-dimensions. To get you started, here are some ideas which you might want to explore.

#### Art medium ideas:

• No need to overcomplicate things, you could stick to colouring pencils or paint on paper
• You could try forming your square grid using paper weaving, or get other ideas from the Art Assignment YouTube channel
• Maybe you want to push the boundaries to traditional media, and try plaiting an automaton into someone’s hair, using coloured beads to make the pattern
• Creating some form of digital art could be the most straightforward option, as the computer can do the drawing for you—just make sure you add your own flair so that it becomes art and is not just a maths plot
• Choose some way to use your automaton to encode musical notes and turn the pattern into a piece of music

#### Automaton ideas:

• The 256 elementary automata are well studied and you can find examples of each online, why not pick one you like the look of and run with it?
• Starting with a row of eight, say, 1s and 0s, you could glue the two ends together and then run your automaton on a cylinder rather than expanding out into the plane
• If you like the idea of ternary, or other base $b$, automata but feel a bit intimidated by the $b^{b^3}$ possible rules, try one of the $b^{3(b-1)+1}$ totalistic rules, where the value of each cell in the next generation depends only on the total sum of the three cells above it, not their individual values and configuration

Ternary totalistic rule 2101001$_3$ which is 1729 in decimal.

• Stephen Wolfram’s book A new kind of science (available for free online) has a whole chapter (chapter 3) on one-dimensional cellular automata and their variations, including totalistic rules, substitution systems, and Turing machines—pick one you like and have a play

We are very excited to see what imaginative things you can come up with. When you’re happy with your piece(s) of art, send them to us on Twitter (@chalkdustmag) using the hashtag #chalkdust13, or via email (contact@chalkdustmagazine.com) and we’ll feature the best ones on our blog.

# Dear Dirichlet, Issue 13

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to deardirichlet@chalkdustmagazine.com.

### Dear Dirichlet,

As a successful author on spies who are also fish, I’m looking to branch out a little. What with the number of streaming platforms, I’m hoping I can get a TV company to make my series of novels into a ten-episode drama. But it feels like a buyers’ market—how can I hook a producer? Let minnow!

— Micholas Herron, Oxford

# Prize crossnumber, Issue 13

Our original prize crossnumber is featured on pages 58 and 59 of Issue 13.

### Rules

• Each clue in this crossnumber contains two statements joined by a logical connective. If the connective is AND, then both the statements are true. If the connective is NAND, then at most one of the statements is true. If the connective is OR, then at least one of the statements is true. If the connective is NOR, then neither of the statements is true. If the connective is XOR, then exactly one of the statements is true. If the connective is XNOR, then either the statements are both true or they are both false.
• Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.
• One randomly selected correct answer will win a £100 Maths Gear goody bag, including non-transitive dice, a Festival of the Spoken Nerd DVD, and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. Maths Gear is a website that sells nerdy things worldwide, with free UK shipping.
• To enter, enter the sum of the across entries below by 18 September 2021. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 November 2021.

# Dear Dirichlet, Issue 12

Moonlighting agony uncle Professor Dirichlet answers your personal problems. Want the prof’s help? Send your problems to deardirichlet@chalkdustmagazine.com.

### Dear Dirichlet,

I have recently entered retirement, having handed over my day job—writing bafflingly popular hyper-violent thrillers which end with the villain getting crushed by an oak bookcase—to my younger brother. But I now find myself with time (as well as coffee and cigarette stains) on my hands. I’m thinking of dipping into movie making. Any good plot ideas?

— Leigh Children, now Wyoming apparently?!

# Prize crossnumber, Issue 12

Our original prize crossnumber is featured on pages 56 and 57 of Issue 12.

### Rules

• Although many of the clues have multiple answers, there is only one solution to the completed crossnumber. As usual, no numbers begin with 0. Use of Python, OEIS, Wikipedia, etc. is advised for some of the clues.
• One randomly selected correct answer will win a £100 Maths Gear goody bag, including non-transitive dice, a Festival of the Spoken Nerd DVD, and much, much more. Three randomly selected runners up will win a Chalkdust T-shirt. Maths Gear is a website that sells nerdy things worldwide, with free UK shipping.
• To enter, enter the sum of the across clues below by 14 March 2021. Only one entry per person will be accepted. Winners will be notified by email and announced on our blog by 1 May 2021.